Basic Continuum Kinematics - Continuum Mechanics of Anisotropic Materials - page 25

O(0)

P

Configuration at t = 0

O(t)

Configuration at time t

THE REAL WORLD EUCLIDEAN 3 D SPACE

Fig. 2.1 Representation of the motion of an object in Euclidean 2D space

x 3

X III

O(0)

(x 1 , x 2 , x 3 )

u

(X I , X II , X III )

O(t)

x

c

X x 2

X II

x 1

X I

Fig. 2.2 Details of the representation in Euclidean 2D space

of a particle is introduced. Each point P O (0) in the continuum model of

the object is labeled by its position in the reference configuration (Fig. 2.2 ).
This procedure assigns a location to each point in the object and such points are
called particles. A position vector of a point in a given coordinate system is a vector
from the origin of coordinates to that point. In this case the reference configuration
is a three-dimensional Cartesian coordinate system with base vectors e a , a ¼ I, II,

III, and coordinates X a ; the position of the particle is described by the vector

X ¼ X a e a :

As a simplifying convention, instead of saying the vector X describes the
position of a particle, we define it to be the particle. Thus the notation X has
replaced the notation P and one can speak of all X

O (0) as a complete represen-

tation of the object in the reference configuration.